Abstract

Small-cell networks (SCNs) technology is being considered as a promising solution to improve the coverage and capacity for small-cell wireless equipment (SWE). However, the deployment of SCNs is challenging due to wireless channel interference, stochastic tasks arrival, and more prominently, the long-term energy consumption constraint of SWEs. In this paper, we provide a novel distributed dynamic resource management approach for energy-aware applications in two-tier SCNs. The joint admission control (AC) at the transport layer and resource allocation (RA) at the physical layer in SWEs is proposed to solve these challenges. Specifically, the AC and RA problem under two-tier SCNs is formulated as a stochastic optimization model which aims at maximizing the long-term average throughput of SWEs in SCN subject to time-average energy consumption limitation of each SWE and network stability constraint. By adopting Lyapunov optimization theory and Lagrangian dual decomposition technique, we propose a distributed online energy-constraint throughput optimal algorithm (ETOA) to obtain optimal AC and RA decisions. Furthermore, we derive the analytical bounds for the time-average system throughput and the time-average queue backlog achieved by our proposed approach under the constraints of long-term average energy consumption and network stability. The evaluation confirms theoretical analysis on the performance of ETOA and also shows that our approach outperforms other resource allocation methods in satisfying the time-average energy consumption requirement of SWEs.

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Acknowledgments

This work is supported in part by the National Key Research and Development Program under Grant no. 2016YFB 1000102, in part by the National Natural Science Foundation of China under Grant no. 61672318, 61631013, and by the QUALCOMM university-sponsored program.

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where the second inequality sign of Eq. 42 holds owing to the fact that the proposed ETOA approach minimizes the RHS of Eq. 14 over all feasible control policy Φ(t) which includes the optimal randomized stationary policy \(\mathbb {\alpha }^{*}(t)\).

Substituting (29) and (30) into (42) and using telescoping sums over all time slots in the above inequality, we obtain the following inequation as δ → 0

Hence, virtual energy queues Eij(t) are mean rate stable based on Definition 1 and thus, the time-average energy consumption constraint C1 is satisfied according to Lemma 1. Similarly, we can prove that data queues Qij(t) are mean rate stable as well.

(b) Since the conclusion Qij(t) < Amax + ν can be proven using similar techniques as [13], we omit the detailed proof here for brevity. Considering the fact that \(\mathbb {E}\left \{L\left ({\Psi }(t)\right )\right \} \ge 0\) and Qij(t) ≥ 0, rearranging (43), we obtain the following inequality